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  1. Discrete tense logic with infinitary inference rules and systematic frame constants: A Hilbert-style axiomatization. [REVIEW]Lennart Åqvist - 1996 - Journal of Philosophical Logic 25 (1):45 - 100.
    The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...)
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  • Eine Logik Erster Stufe mit Einem Infinitären Zeitoperator.Hiroya Kawai - 1982 - Mathematical Logic Quarterly 28 (13):173-180.
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  • Loop-Check Specification for a Sequent Calculus of Temporal Logic.Romas Alonderis, Regimantas Pliuškevičius, Aida Pliuškevičienė & Haroldas Giedra - 2022 - Studia Logica 110 (6):1507-1536.
    In our previous work we have introduced loop-type sequent calculi for propositional linear discrete tense logic and proved that these calculi are sound and complete. Decision procedures using the calculi have been constructed for the considered logic. In the present paper we restrict ourselves to the logic with the unary temporal operators “next” and “henceforth always”. Proof-theory of the sequent calculus of this logic is considered, focusing on loop specification in backward proof-search. We describe cyclic sequents and prove that any (...)
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